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A367216
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Number of subsets of {1..n} whose cardinality is equal to the sum of some subset.
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24
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1, 2, 3, 5, 10, 20, 40, 82, 169, 348, 716, 1471, 3016, 6171, 12605, 25710, 52370, 106539, 216470, 439310, 890550, 1803415, 3648557, 7375141, 14896184, 30065129, 60639954, 122231740, 246239551
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OFFSET
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0,2
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LINKS
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FORMULA
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EXAMPLE
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The a(0) = 1 through a(4) = 10 subsets:
{} {} {} {} {}
{1} {1} {1} {1}
{1,2} {1,2} {1,2}
{2,3} {2,3}
{1,2,3} {2,4}
{1,2,3}
{1,2,4}
{1,3,4}
{2,3,4}
{1,2,3,4}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], MemberQ[Total/@Subsets[#], Length[#]]&]], {n, 0, 10}]
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CROSSREFS
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The following sequences count and rank integer partitions and finite sets according to whether their length is a subset-sum or linear combination of the parts. The current sequence is starred.
sum-full sum-free comb-full comb-free
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A000009 counts subsets summing to n.
A000124 counts distinct possible sums of subsets of {1..n}.
A240855 counts strict partitions whose length is a part, complement A240861.
Triangles:
A365541 counts sets containing two distinct elements summing to k.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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